Decoding the Antikythera Mechanism: Investigation of an Ancient Astronomical Calculator
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Decoding the Antikythera Mechanism: Investigation of an Ancient Astronomical Calculator T. Freeth 1,2 , Y. Bitsakis 3,5 , X. Moussas 3, J.H. Seiradakis 4, A.Tselikas 5, E. Magkou 6, M. Zafeiropoulou 6, R. Hadland 7, D. Bate 7, A. Ramsey 7, M. Allen 7, A. Crawley 7, P. Hockley 7, T. Malzbender 8, D. Gelb 8, W. Ambrisco 9 and M.G. Edmunds 1 1 Cardiff University, School of Physics and Astronomy, Queens Buildings, The Parade, Cardiff CF24 3AA, UK. Mike Edmunds Mike.Edmunds @ astro.cf.ac.uk 2 Images First Ltd 10 Hereford Road, South Ealing, London W5 4SE, UK. Tony Freeth tony @ images- first.com 3 National & Kapodistrian University of Athens, Department of Astrophysics, Astronomy and Mechanics, Panepistimiopolis, GR15783, Zographos, Greece. Xenophon Moussas, xmoussas @ phys.uoa.gr 4 Aristotle University of Thessaloniki, Department of Physics, Section of Astrophysics, Astronomy and Mechanics, GR-54124 Thessaloniki, Greece. John Seiradakis jhs @ astro.auth.gr 5 Centre for History and Palaeography, National Bank of Greece Cultural Foundation, P. Skouze 3, 10560 Athens, Greece. Yanis Bitsakis bitsakis @ gmail.com 6 National Archaeological Museum of Athens, 44 Patission Str, 106 82 Athens, Greece. 7 X-Tek Systems Ltd, Tring Business Centre, Icknield Way, Tring, Herts HP23 4JX, UK. 8 Hewlett-Packard Laboratories, 1501 Page Mill Road, Palo Alto, CA 94304, USA. 9 Foxhollow Technologies Inc., 740 Bay Road, Redwood City, CA 94063, USA. Decoding the Antikythera Mechanism , published in Nature, Volume 444, Issue 7119, pp. 587-591 (2006). 1 The Antikythera Mechanism is a unique Greek geared device, constructed around the end of the 2nd Century BC. From previous work 1,2,3,4,5,6,7,8,9 it is known that it calculated and displayed celestial information, particularly cycles such as the phases of the moon and a luni-solar calendar. Calendars were important to ancient societies 10 for timing agricultural activity and fixing religious festivals. Eclipses and planetary motions were often interpreted as omens, while the calm regularity of the astronomical cycles must have been philosophically attractive in an uncertain and violent world. Named after its place of discovery in 1901 in a Roman shipwreck, the Mechanism is technically more complex than any known device for at least a millennium afterwards. Its specific functions have remained controversial 11,12,13,14 because its gears and the inscriptions upon its faces are only fragmentary. Here we report surface imaging and high-resolution X- ray tomography of the surviving fragments, enabling us to reconstruct the gear function and double the number of deciphered inscriptions. The Mechanism predicted lunar and solar eclipses based on Babylonian arithmetic-progression cycles. The inscriptions support suggestions of mechanical display of planetary positions 9,14,16 , now lost. In the second century BC, Hipparchos developed a theory to explain the irregularities of the Moon's motion across the sky caused by its elliptic orbit. We find a mechanical realization of this theory in the gearing of the Mechanism, revealing an unexpected degree of technical sophistication for the period . Decoding the Antikythera Mechanism , published in Nature, Volume 444, Issue 7119, pp. 587-591 (2006). 3 The bronze Mechanism (Figure 1), probably hand-driven, was originally housed in a wooden-framed case 1 of (uncertain) overall size 340 x 180 x 90 mm. It had front and back doors, with astronomical inscriptions covering much of the exterior of the Mechanism (Figure 2). Our new transcriptions and translations of the Greek texts are given in Supplementary Notes 2 (Glyphs & Inscriptions). The detailed form of the lettering can be dated to the second half of the 2 nd Century BC, implying that that the Mechanism was constructed during the period 150- 100 BC, slightly earlier than previously suggested 1. This is consistent with a date of around 80-60 BC of the wreck 1,20 from which the mechanism was recovered by some of the first underwater archaeology. We are able to complete the reconstruction 1 of the Back Door inscription with text from fragment E, and characters from fragments A and F. The Front Door is mainly from fragment G. The text is astronomical with many numbers that could be related to planetary motions. The use of “sterigmos [ ΣΤΗΡΙΓΜΟΣ] – station or stationary point” means where a planet’s apparent motion changes direction and the numbers may relate to planetary cycles. The Back Door inscription mixes mechanical terms about construction (“trunnions”, “gnomon”, “perforations”) with astronomical periods. Of the periods, 223 is the Saros eclipse cycle (see Box for brief explanation of astronomical cycles and periods). We discover the inscription “spiral divided into 235 sections”, which is the key to understanding the function 6 of the Upper Back Dial. The references to “golden little sphere” and “little sphere” probably refer to the front zodiac display for the Sun and Moon – including phase for the latter. The text near the Lower Back Dial includes “Pharos” and “From South (about/around)….Spain ten”. These geographical references, together with previous readings 1 of “Towards the East”, “West-North-West” and “West-South-West” suggest an eclipse function for the dial, since solar eclipses occur only at limited geographical sites, and winds were often recorded 22,23,24 in antiquity with eclipse observations. Possibly this information was added to the Mechanism during use. Turning to the dials themselves, the Front Dial displays the position of the Sun and Moon in the Zodiac, and a corresponding calendar 1 of 365 days that could be adjusted for leap years. Previously 1, it was suggested that the Upper Back Dial might have five concentric rings with 47 divisions per turn, showing the 235 months of the 19- year Metonic Cycle. A later proposal 5 augments this with the Upper Subsidiary Dial showing the 76-year Callippic Cycle. Our optical and CT imaging confirm these proposals, with 34 scale markings discovered on the Upper Back Dial. Based on a statistical analysis analogous to that described for gear tooth counts below, we confirm the 235 total divisions. We also find from the CT that the subsidiary dial is indeed divided into quadrants 1,6 , as required for a Callippic Dial. In agreement with the Back Door inscription, we also substantiate the perceptive proposal 5,25 that the dial is in fact a spiral, made from semicircular arcs displaced to two centres on the vertical midline. In the CT of fragment B we find a new feature that explains why the dial is a spiral: a “Pointer-Follower” device (see Figure 3) travelled around the spiral groove to indicate which month (across the five turns of the scale) should be read. From our CT data of the 48 scale divisions observed in fragments A, E and F, we establish 223 divisions in the four-turn 5,25 spiral on the Lower Back Dial, the spiral starting at the bottom of the dial. This is the Saros eclipse cycle, whose number is on the Back Door inscription. The 54-year Exeligmos cycle of three Saros cycles is shown on the Lower Subsidiary Dial. Between the scale divisions of the Saros Dial we have identified 16 blocks of characters, or “glyphs” (see Supplementary Notes 2 (Glyphs & Inscriptions)) at intervals of one, five and six months. These are eclipse predictions and contain either Σ for a lunar eclipse (from ΣΕΛΗΝΗ, Moon) or H for a solar eclipse (from ΗΛΙΟΣ, Sun) or both. A correlation analysis (analogous to DNA sequence matching) with historic eclipse data 26 indicates that over a period of 400 – 1 BC the sequence of eclipses marked by the identified glyphs would be exactly matched by 121 possible start dates. The matching only occurs if the lunar month starts at first crescent and confirms this choice of month start in the Mechanism. The sequences of eclipses can then be used to predict the expected position of glyphs on the whole dial, as seen in Figure 4. The dial starts and finishes with an eclipse. Although Ptolemy indicates that the Greeks recorded eclipses in the 2 nd century BC, the Babylonian Saros Canon 22,23,24 is the only known source of sufficient data to construct the dial. Decoding the Antikythera Mechanism , published in Nature, Volume 444, Issue 7119, pp. 587-591 (2006). 4 The functions of the Mechanism are determined by the tooth counts of the gears. These are based mainly on the CT, using angular measurement from a nominal centre to the remains of tooth tips. In a few cases all teeth can be seen, but many gears are incomplete. Counts are established by fitting models with regularly spaced teeth and minimising the r.m.s. deviation from the measurements—varying the centre in software (when unclear) to find the best-fit solution or solutions (see Supplementary Notes 3 (Gears)). We have adopted a systematic nomenclature of lower case letters for the axis of the gear, with numbering increasing with ordering from the front of the Mechanism. Hypothetical (lost) gears are denoted by italics. Several models have been proposed for the gear trains1,2,4,5,6,8 . We agree with the assumption of four missing gears ( n1, n2, p1, p2 ) to drive the Metonic and Callippic Dials 4. We propose a new reconstruction for the other trains, which uses all extant gears (except the lone r1 from the separate fragment D). The proposed model is shown in Figure 5. We require the assumption of only one further gear ( m3) whose proposed shaft is clearly broken off in the CT. A detailed description is contained in the Supplementary Notes 3 (Gears). Of particular note is the dual use of the large gear, e3, at the back of the Mechanism, which has found no use in previous models.